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Homework Help: Find La Placian of a function in cartesian and Spherical Coordinates

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Prove the La Placian of V(x,y,z)=(zx[itex]^{2}[/itex])/(x[itex]^{2}[/itex]+y[itex]^{2}[/itex]+z[itex]^{2}[/itex]) in Cartesian coordinates is equal to that in Spherical coordinates

    2. Relevant equations


    3. The attempt at a solution

    I have attempted to calculate all the terms out, and there were A LOT. I was hoping the derivatives in Cartesian, which I did first, would cancel, but they didn't. I may have made a mistake, I used the product rule and came up with 6 terms in the numerator over (x[itex]^{2}[/itex]+y[itex]^{2}[/itex]+z[itex]^{2}[/itex])[itex]^{3}[/itex]. Any suggestions? Spherical was even more complicated... I had the following:
    r(cosθ)[itex]^{2}[/itex](sin[itex]\phi[/itex])[itex]^{2}[/itex](cos[itex]\phi[/itex]) before I began taking partial derivatives. Any help would really be appreciated, thanks...
    Last edited: Feb 16, 2013
  2. jcsd
  3. Feb 17, 2013 #2


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    Re: Find La Placian of a function in cartesian and Spherical Coordinat

    Which convention for spherical coordinates are you using? Physicists typically use ##\theta## as the angle from the z-axis whereas mathematicians use ##\phi##. Your expression for ##V(r,\theta,\phi)## appears to be using the math convention. I just ask because you posted this in the physics section.

    No suggestions, by the way. I think you just have to grind it out.
  4. Feb 17, 2013 #3
    Re: Find La Placian of a function in cartesian and Spherical Coordinat

    This problem is from a physics class, and the class doesn't have a book assigned...so I've been looking through my calc iv book to try and get some information. Thanks for pointing out there are different systems, I wasn't aware of that and my professor didn't mention it...
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